A multiple choice test has 49 questions. Each question has 3 possible answers, o
ID: 3309821 • Letter: A
Question
A multiple choice test has 49 questions. Each question has 3 possible answers, one of which is correct. Two points are given for each correct answer, but a point is taken off for an incorrect answer.
(a) In order to pass the test, a student must answer 20 questions correctly. If a student answers all the questions by randomly guessing, what is the chance of passing? (Hint: the number of questions answered correctly is the sum of 49 numbers taken from a zero/one box; the fraction of zeros and ones in the box depends on chances of answering a question correctly.)
(b) Suppose 5 friends decide to randomly guess their way through the test. About how many of them should pass the test? Explain (Hint: The number of friends who pass the test is the sum of 5 numbers from a zero/one box; the number of zeros and ones in the box depends on the chance of passing the test from part (a) ).
(c) Suppose the teacher revises the plan and decides that in order to pass the test, a student must score at least 10 points on the test. If a student answers all questions by randomly guessing, what is the chance of passing?
(d) Suppose the teacher wants to double the chance of passing. What should she require in terms of points needed for passing?
Explanation / Answer
a)
the prob of answering correctly is 0.33
Pr[20 > x]=0.1558
b)
0.15*5 ~ 1 student should pass the test
c)
In order to score atleast 10 point he should have atleast 20 correct answers
Pr[20 > x]=0.1558
d)
In order to double the chance of passing the points needed should be 5 which will result from atleast 18 correct answers when all questions are answered
Pr[18 > x]=0.338
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